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Yes; this is given in Mines, Richman, RuitenbergRuitenburg, A course in constructive algebra, on p.54, stated just before Lemma 4.1, and proved in that lemma by a Church-Rosser argument. (Thanks to Thierry Coquand for pointing me to this proof.)

Yes; this is given in Mines, Richman, Ruitenberg, A course in constructive algebra, on p.54, stated just before Lemma 4.1, and proved in that lemma by a Church-Rosser argument. (Thanks to Thierry Coquand for pointing me to this proof.)

Yes; this is given in Mines, Richman, Ruitenburg, A course in constructive algebra, on p.54, stated just before Lemma 4.1, and proved in that lemma by a Church-Rosser argument. (Thanks to Thierry Coquand for pointing me to this proof.)

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Yes; this is given in Mines, Richman, Ruitenberg, A course in constructive algebra, on p.54, stated just before Lemma 4.1, and proved in that lemma by a Church-Rosser argument. (Thanks to Thierry Coquand for pointing me to this proof.)